The Ramsey numbers R(Tn, W6) for small n

Abstract

Let T_n denote a tree of order n and W_m a wheel of order m + 1. Baskoro et al. conjectured in [2] that if T_n is not a star, then R(T_n, W_m) = 2n - 1 for m ≥ 6 even and n ≥ m -1. We disprove the Conjecture in [6]. In this paper, we determine R(T _n,W₆) for n ≤ 8 which is the first step for us to determine R(T_n, W₆) for any tree T_n.